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A small steel ball of radius r is allowe...

A small steel ball of radius r is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity `eta`. After some time the velocity of the ball attains a constant value known as terminal velocity `upsilon_T`. The terminal velocity depends on (i) the mass of the ball m (ii) `eta`, (iii) r and (iv) acceleration due to gravity g . Which of the following relations is dimensionally correct?

A

`v_(T)prop(mg)/(etar)`

B

`v_(T)prop(etar)/(mg)`

C

`v_(T)propetarmg`

D

`v_(T)prop(mgr)/(eta)`

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The correct Answer is:
A
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